Interactions of quantum affine algebras with cluster algebras, current algebras and categorification, Kruse, Rudolf Mostaghim, Sanaz Borgelt, Christian Braune, Christian Steinbrecher, Matthias
Описание: This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: * String diagrams and categorification * Quantum affine algebras and cluster algebras * Steinberg groups for Jordan pairs * Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.
Автор: Vladimir K. Dobrev Название: AdS/CFT, (Super-)Virasoro, Affine (Super-)Algebras ISBN: 3110609681 ISBN-13(EAN): 9783110609684 Издательство: Walter de Gruyter Цена: 18586.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.
Автор: Bogdan Ion, Siddhartha Sahi Название: Double Affine Hecke Algebras and Congruence Groups ISBN: 1470443260 ISBN-13(EAN): 9781470443269 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 10659.00 р. Наличие на складе: Нет в наличии.
Автор: Nanhua Xi Название: Representations of Affine Hecke Algebras ISBN: 3540583890 ISBN-13(EAN): 9783540583899 Издательство: Springer Рейтинг: Цена: 3487.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: These lecture notes show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. The based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras.
Автор: A.A. Kirillov; A.A. Kirillov; V. Soucek; Yu.A. Ner Название: Representation Theory and Noncommutative Harmonic Analysis I ISBN: 3540186980 ISBN-13(EAN): 9783540186984 Издательство: Springer Рейтинг: Цена: 19564.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This two-part survey provides a short review of the classical part of representation theory, carefully exposing the structure of the theory without overwhelming readers with details, and deals with representations of Virasoro and Kac-Moody algebra. It presents a wealth of recent results on representations of infinite-dimensional groups.
Автор: Adamovic Drazen, Papi Paolo Название: Affine, Vertex and W-Algebras ISBN: 3030329089 ISBN-13(EAN): 9783030329082 Издательство: Springer Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory.
Автор: Dra?en Adamovi?; Paolo Papi Название: Affine, Vertex and W-algebras ISBN: 3030329054 ISBN-13(EAN): 9783030329051 Издательство: Springer Рейтинг: Цена: 13974.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book focuses on recent developments in the theory of vertex algebras, with particular emphasis on affine vertex algebras, affine W-algebras, and W-algebras appearing in physical theories such as logarithmic conformal field theory. It is widely accepted in the mathematical community that the best way to study the representation theory of affine Kac–Moody algebras is by investigating the representation theory of the associated affine vertex and W-algebras. In this volume, this general idea can be seen at work from several points of view. Most relevant state of the art topics are covered, including fusion, relationships with finite dimensional Lie theory, permutation orbifolds, higher Zhu algebras, connections with combinatorics, and mathematical physics. The volume is based on the INdAM Workshop Affine, Vertex and W-algebras, held in Rome from 11 to 15 December 2017. It will be of interest to all researchers in the field.
Автор: Julius Jellinek Название: Theory of Atomic and Molecular Clusters ISBN: 3642635709 ISBN-13(EAN): 9783642635700 Издательство: Springer Рейтинг: Цена: 14365.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study.The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Math?matiques Pures et Appliqu?es) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck.
The courses held were:
Advanced homological algebra Introduction to the representation theory of algebras Auslander-Reiten theory for algebras of infinite representation type Cluster algebras arising from surfaces Cluster tilted algebras Cluster characters Introduction to K-theory Brauer graph algebras and applications to cluster algebras
Описание: This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras.
Автор: Chun-Ju Lai, Li Luo, Weiqiang Wang, Yiqiang Li, Zhaobing Fan Название: Affine Flag Varieties and Quantum Symmetric Pairs ISBN: 1470441756 ISBN-13(EAN): 9781470441753 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 12058.00 р. Наличие на складе: Нет в наличии.
Описание: Demonstrates that the quantum groups arising from Lusztig algebras and Schur algebras via stabilization procedures are (idempotented) coideal subalgebras of quantum groups of affine $\mathfrak{sl}$ and $\mathfrak{gl}$ types, respectively. In this way, the authors provide geometric realizations of eight quantum symmetric pairs of affine types.
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